1. What similarities and differences do you see between functions and linear equations?  Are all linear equations functions?

A linear equation is an algebraic expression which has a either a constant of a variable, for example y = 2x + 3. A function is composed of ordered pairs and each pair is related, for example f={(1,2),(3,4),(5,6)}.

All linear equations are functions since the values in the functions may be solved using through the linear equation.

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2. Is there an instance when a linear equation is not a function? Support your answer.

No, all linear equations are functions. For example, consider:

Linear equation y = 2x+3

x = 1               y = 2(1) + 3     = 5

x = 2               y = 2(2) + 3     = 7

x = 3               y = 2(3) + 3     = 9

Therefore, the elements of function f are {(1,5),(2,7),(3,9)}.

Create an equation of a nonlinear function and provide two inputs to evaluate.

Nonlinear function y = 2×2 + x + 5

Sample evaluation:

x = 2               y = 2(2)2 + 2 + 5         = 15

x = 4               y = 2(4)2 + 4 + 5         = 41
3. What is the difference between domain and range? Describe a real-life situation that could be modeled by a function.

The domain of a function is the set of possible values of the independent variable while the range is the complete set of values of the dependent variable in a function (http://www.intmath.com/Functions-and-graphs/2a_Domain-and-range.php). For example, in a group of 25 students in a class – 12 of which are males and 13 are females. If a function is to be created, each male may be paired with a female student. One male student may have 2 female partners. In this example, the domain is composed of the male students and the range is the female students.

4. Describe the values for x that may not be appropriate values even when they are defined by someone’s function. A function could, for example, indicate the amount of bone strength (y) in a living human body over time in years (x).

The bone strength (y) is dependent on the living human body over time (x). In the case presented, the value of x may not be less than 1 and not greater than 100. It would not make sense to look at negative years, because the person would not yet be born. Likewise, looking beyond 100 years might not make sense, as many people do not live to be 100.

5. How can you determine if two lines are perpendicular?

Two lines are perpendicular if they intersect at one another.

6. Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which methods do you like best? Why? What circumstances would cause you to use a different method?

Solving an equation using the graphing method is much easier to use because you only have to assume a value for x and immediately, by following the equation, y is solved and also in illustration, the values of the function is clearly shown. While in using the substitution or elimination, this needs an ample amount of time because you still have to eliminate the variable one at a time.

I would prefer to solve the equation using graphs because I just have to assume values for x and y is solved. Using the elimination or substitution method, I might commit errors in eliminating a variable.

7. Describe what the graph of interval [-4, 10] looks like.

The graph of [-4, 10] is inclined towards the 2nd quadrant. The function may have values –+x and -+y.

Reference:

No Author. (No Year). Domain and Range of Function. Retrieved on September 16, 2008 at http://www.intmath.com/Functions-and-graphs/2a_Domain-and-range.php.

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